full_governance_unique
plain-language theorem explainer
Exactly one governance assignment satisfies all three binary criteria simultaneously. Institutional theorists modeling configDim D=5 would cite this uniqueness to derive the five canonical institutions from the impossibility of any single body meeting every criterion. The proof is a direct computation that enumerates the finite space of assignments and counts the matches.
Claim. The set of all possible governance assignments has cardinality one when filtered to those equal to the full triple: $|{a : GovernanceAssignment | a = (true, true, true)}| = 1$.
background
The module treats governance as a structure forced by configDim D=5, which produces exactly five canonical institutions (executive, legislative, judicial, military, press) and five corresponding failure modes. GovernanceAssignment is the type of boolean triples recording satisfaction of the three binary criteria; fullGovernance is the concrete triple that sets every coordinate to true. The upstream definition fullGovernance supplies this distinguished assignment, and the module notes the parallel to Arrow's theorem: no single institution can satisfy all three criteria at once.
proof idea
The proof is a one-line wrapper that applies the decide tactic to evaluate the cardinality of the Finset filter over the universe of all possible assignments.
why it matters
The result is packaged directly into the governanceDesignCert definition, which records the five-institution count, five-failure-mode count, three-criterion count, and this uniqueness property. It thereby completes the E7 governance-design step in the Recognition Science chain, confirming that configDim D=5 forces the classical five-institution structure.
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